Numerical study on Kerr frequency comb generation in Si₃N₄ microresonators with frequency-dependent access coupler properties

Abstract

Within the frame of vertically coupled silicon nitride (Si3N4) resonators characterized with 220 GHz free spectral range driven by a continuous wave laser at 1.55 µm for Kerr comb generation, the design of achromatic critically coupled resonators may bring severe issues because of the difficulty in designing dispersion-free access couplers with controlled coupling factor over a large spectral bandwidth. As a consequence of this, numerical simulations of Kerr frequency comb in these structures may drastically differ from reality if frequency-dependence of the access coupler's properties is not taken into account in the simulated model. In order to address this issue, we have developed a numerical model that takes into account the frequency dependence of the access coupler coefficients and remains valid even for the simulation of low Q factor resonators. Field propagation within the ring is described by the nonlinear Schrödinger equation. Novelty in the model resides in the computation of a complex-valued, frequency dependent coupling transfer function between resonant ring and underlying access waveguide that models frequency-dependent dispersion and losses in the access coupling region of the resonator. Based on simulation results, we discuss on the differences observed in Kerr comb generation in resonators with three different coupler designs initially intended to yield critical coupling over the largest achievable bandwidth.